Autocorrelation And The ACF
Autocorrelation measures how similar a series is to a shifted copy of itself. The shift amount is called a lag.
Reading correlation by lag
- At lag one, you compare each value with the one just before it.
- At lag twelve on monthly data, you compare each value with the same month last year.
- A high value at a lag means the past strongly predicts the present at that distance.
The ACF plot
The autocorrelation function plots correlation against lag. It is one of the most useful diagnostics in time series work.
- A slow decay across many lags suggests a trend that has not been removed.
- Spikes at seasonal lags reveal a repeating cycle.
- Values inside the confidence band are treated as effectively zero.
The partial version
The partial autocorrelation function strips out the influence of shorter lags, isolating the direct link at each lag. Analysts use both plots together to pick model orders.
Key idea
The ACF shows how strongly each lag predicts the present, guiding both diagnosis and model choice.